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[[80,16,4]] d =
n
80
k
16
d
4
kd²/n
3.2
w
12
X/Z
1

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Distance

X/Z asymmetry 1 · d_X = 4, d_Z = 4 · w_X = 12, w_Z = 12 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 4 · witness weight 4 (claimed upper_bound)
witness operator (support, 4 qubits)
[50, 51, 54, 55]
d_Z 4 · witness weight 4 (claimed upper_bound)
witness operator (support, 4 qubits)
[25, 33, 41, 49]
certificate exact, d = 4 · scipy/HiGHS MILP
X: no logical < 4 exists; Z: no logical < 4 exists

Diagnostics

computed by the verifier from the parity checks, the layout, and the stored witnesses; shown as evidence, not used for ranking
girth H_X 4 · H_Z 4 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)
check weights H_X 5–12 (mean 7.5) · H_Z 5–12 (mean 7.5)
qubit degrees H_X 1–8 (mean 3.0) · H_Z 1–8 (mean 3.0)
trapping sets H_X (1,1)×8 (2,1)×96 (3,1)×56 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,1): 8 (1,2): 24 (1,3): 24 (1,4): 20 (1,8): 4 (2,1): 96 (2,2): 96 (2,3): 44 (2,4): 96 (2,5): 108 (2,6): 48 (2,7): 8 (2,8): 48 (2,9): 72 (2,10): 32 (3,1): 56 (3,2): 186 (3,3): 444 (3,4): 828 (3,5): 1242 (3,6): 1114 (3,7): 1014 (3,8): 984 (3,9): 1184 (3,10): 1140 (3,11): 752 (3,12): 256 (3,14): 24 (3,15): 72 (3,16): 48
trapping sets H_Z (1,1)×8 (2,1)×96 (3,1)×56 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,1): 8 (1,2): 24 (1,3): 24 (1,4): 20 (1,8): 4 (2,1): 96 (2,2): 96 (2,3): 44 (2,4): 96 (2,5): 108 (2,6): 48 (2,7): 8 (2,8): 48 (2,9): 72 (2,10): 32 (3,1): 56 (3,2): 186 (3,3): 444 (3,4): 828 (3,5): 1242 (3,6): 1114 (3,7): 1014 (3,8): 984 (3,9): 1184 (3,10): 1140 (3,11): 752 (3,12): 256 (3,14): 24 (3,15): 72 (3,16): 48

Construction & provenance

authors @mathysrennela
provenance submitted through the challenge
novelty novelty not audited
construction Hypergraph product of classical codes eham8 and eham8
model Tencent Hy3 (claimed, not verified)
builds on arXiv:0903.0566
date 2026-07-17
family hypergraph product (a tag, not a ranking)
locality unrestricted (computed from the layout)
weight class weight > 8 (computed)

How this code was found

no research note was staged with this submission — notes are requested for new submissions (notes/README.md)

Parity checks

X-checks 32 (max weight 12) · Z-checks 32 (max weight 12)
H_X (32 checks, sparse supports)
[0, 16, 32, 48, 64, 67] [1, 17, 33, 49, 65, 67] [2, 18, 34, 50, 64, 65, 67] [3, 19, 35, 51, 66, 67] [4, 20, 36, 52, 64, 66, 67] [5, 21, 37, 53, 65, 66, 67] [6, 22, 38, 54, 64, 65, 66, 67] [7, 23, 39, 55, 67] [8, 16, 40, 48, 68, 71] [9, 17, 41, 49, 69, 71] [10, 18, 42, 50, 68, 69, 71] [11, 19, 43, 51, 70, 71] [12, 20, 44, 52, 68, 70, 71] [13, 21, 45, 53, 69, 70, 71] [14, 22, 46, 54, 68, 69, 70, 71] [15, 23, 47, 55, 71] [24, 32, 40, 48, 72, 75] [25, 33, 41, 49, 73, 75] [26, 34, 42, 50, 72, 73, 75] [27, 35, 43, 51, 74, 75] [28, 36, 44, 52, 72, 74, 75] [29, 37, 45, 53, 73, 74, 75] [30, 38, 46, 54, 72, 73, 74, 75] [31, 39, 47, 55, 75] [0, 8, 16, 24, 32, 40, 48, 56, 76, 79] [1, 9, 17, 25, 33, 41, 49, 57, 77, 79] [2, 10, 18, 26, 34, 42, 50, 58, 76, 77, 79] [3, 11, 19, 27, 35, 43, 51, 59, 78, 79] [4, 12, 20, 28, 36, 44, 52, 60, 76, 78, 79] [5, 13, 21, 29, 37, 45, 53, 61, 77, 78, 79] [6, 14, 22, 30, 38, 46, 54, 62, 76, 77, 78, 79] [7, 15, 23, 31, 39, 47, 55, 63, 79]
H_Z (32 checks, sparse supports)
[0, 2, 4, 6, 64, 76] [1, 2, 5, 6, 65, 77] [3, 4, 5, 6, 66, 78] [0, 1, 2, 3, 4, 5, 6, 7, 67, 79] [8, 10, 12, 14, 68, 76] [9, 10, 13, 14, 69, 77] [11, 12, 13, 14, 70, 78] [8, 9, 10, 11, 12, 13, 14, 15, 71, 79] [16, 18, 20, 22, 64, 68, 76] [17, 18, 21, 22, 65, 69, 77] [19, 20, 21, 22, 66, 70, 78] [16, 17, 18, 19, 20, 21, 22, 23, 67, 71, 79] [24, 26, 28, 30, 72, 76] [25, 26, 29, 30, 73, 77] [27, 28, 29, 30, 74, 78] [24, 25, 26, 27, 28, 29, 30, 31, 75, 79] [32, 34, 36, 38, 64, 72, 76] [33, 34, 37, 38, 65, 73, 77] [35, 36, 37, 38, 66, 74, 78] [32, 33, 34, 35, 36, 37, 38, 39, 67, 75, 79] [40, 42, 44, 46, 68, 72, 76] [41, 42, 45, 46, 69, 73, 77] [43, 44, 45, 46, 70, 74, 78] [40, 41, 42, 43, 44, 45, 46, 47, 71, 75, 79] [48, 50, 52, 54, 64, 68, 72, 76] [49, 50, 53, 54, 65, 69, 73, 77] [51, 52, 53, 54, 66, 70, 74, 78] [48, 49, 50, 51, 52, 53, 54, 55, 67, 71, 75, 79] [56, 58, 60, 62, 76] [57, 58, 61, 62, 77] [59, 60, 61, 62, 78] [56, 57, 58, 59, 60, 61, 62, 63, 79]
Code ID 80-16-4 · download JSON · raw on GitHub